Finite Group Databasebeta

← #10827366

Subgroups — #10827366

Order 768.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5565C211yesmaximal, characteristic, complemented
2C3×#2407C211yesmaximal, characteristic, complemented
3C2×#5238C211yesmaximal, characteristic, complemented
4C2×#5233C211yesmaximal, characteristic, complemented
5#71699C211yesmaximal, characteristic, complemented
6#71692C211yesmaximal, characteristic, complemented
7#71684C211yesmaximal, characteristic, complemented
8#71677C211yesmaximal, characteristic, complemented
9#71610C211yesmaximal, characteristic, complemented
10#69687C211yesmaximal, characteristic, complemented
11#69669C211yesmaximal, characteristic, complemented
12#69657C211yesmaximal, characteristic, complemented
13#69639C211yesmaximal, characteristic, complemented
14#69515C211yesmaximal, characteristic, complemented
15#69503C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#939—21no—
23C22×#213C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#926C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29#5565—24no—
30#5565—24no—
31C2×#898—21no—
32C2×#883—21no—
33C2×#67⋊C4—21no—
34C2×C4×D12C2211yescharacteristic
35C2×#870C2211yescharacteristic
36C3×#394—21no—
37C3×#392—21no—
38C3×#391C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C3×#386—21no—
41C3×#385—21no—
42C3×#380C2211yescharacteristic
43#5238—24no—
44#5233—24no—
45C2×#835C2211yescharacteristic
46C2×#835C2211yescharacteristic
47C2×#835C2211yescharacteristic
48C2×#832C2211yescharacteristic
49C2×#832C2211yescharacteristic
50C2×#832C2211yescharacteristic
51C2×#830C2211yescharacteristic
52C2×#830C2211yescharacteristic
53C2×#830C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56#4529C2211yescharacteristic
57#4529C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#553—31no—
65C2×#449—31no—
66C2×#416—31no—
67#2407D311yescharacteristic, complemented
68#2026—31no—
69#2025—31no—
70#2000—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1877—31no—
75#1874—31no—
76#1872—31no—
77#1869—31no—
78#1825—31no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4D411yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C22×#67—21no—
94C22×#67—21no—
95C23×Dic3—21no—
96C22×D12C2311yescharacteristic
97C22×C4×D3—21no—
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8—41no—
100C3×#121—22no—
101C3×#121—41no—
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4D411yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4D411yescharacteristic
114C2×C3×C22⋊C4D411yescharacteristic
115C2×C3×C42C2311yescharacteristic
116C2×#217—21no—
117C2×#215—22no—
118C2×#215—22no—
119C2×#215—41no—
120#939—28no—
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—41no—
124#930—22no—
125#930—22no—
126#930—22no—
127#930D414yescomplemented
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131#926—22no—
132#926D414yescomplemented
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3—22no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×C4×Dic3—21no—
142C22×C3⋊C8—22no—
143C22×C3⋊C8—41no—
144C22×C3⋊C8—41no—
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149#898—28no—
150#883—28no—
151#67⋊C4—28no—
152C4×D12—22no—
153C4×D12—22no—
154#870—22no—
155#870—22no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159#835—22no—
160#835—22no—
161#835—22no—
162#832—22no—
163#832—22no—
164#832—22no—
165#830—22no—
166#830—41no—
167#830—41no—
168#809—41no—
169#809—41no—
170C22×#41C2×D311yescharacteristic
171C22×SD16—31no—
172C22×D8—31no—
173C23×C8—31no—
174#553—64no—
175#553—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#123—61no—
179C2×C22⋊Q8C2×D311yescharacteristic
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—61no—
183C2×#121C2×D311yescharacteristic
184C2×C4×D4—31no—
185C2×C4×D4—61no—
186C2×C4×D4C2×D311yescharacteristic
187C2×#117—31no—
188C22×C4⋊C4—31no—
189#449—64no—
190#416—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202#394—21no—
203#392—21no—
204#391C2×D311yescharacteristic
205#390C2×D311yescharacteristic
206#386—21no—
207#385—21no—
208#380C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C24×C3C2×D411yescharacteristic
220C23×D3—21no—
221C3×#41—28no—
222C3×#41—44no—
223C3×#41—44no—
224C3×#41—44no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8#4112yes—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—41no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4—81no—
245C2×C3×D4#4112yes—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4—42no—
262C22×C3×C4C2×D412yes—
263C22×C3×C4C2×D412yes—
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C2×#67—24no—
270C2×#67—24no—
271C2×#67—42no—
272C2×#67—42no—
273C2×#67—81no—
274C2×#67—81no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—24no—
279C22×Dic3—81no—
280C22×Dic3—81no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12C2×D412yes—
287C2×C4×D3—24no—
288C2×C4×D3—81no—
289C2×C4×D3—81no—
290C3×C4⋊C4—22no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—42no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—42no—
299C3×C22⋊C4—42no—
300C3×C22⋊C4—42no—
301C3×C22⋊C4—81no—
302C3×C22⋊C4—81no—
303C3×C42—21no—
304C3×C42—21no—
305#217—24no—
306#215—44no—
307#213—44no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—24no—
311C4⋊Dic3—24no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3C2×D412yes—
316C4⋊Dic3C2×D412yes—
317C4⋊Dic3C2×D412yes—
318Dic3⋊C4—24no—
319Dic3⋊C4—24no—
320C4×Dic3—24no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—44no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—41no—
339C2×#41—41no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4#6711yescharacteristic
347C22×D4C22×D311yescharacteristic
348C23×C4—21no—
349C23×C4—61no—
350C23×C4—61no—
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×D8—62no—
357C2×D8—62no—
358C2×D8—121no—
359C22×C8—31no—
360C22×C8—31no—
361C22×C8—31no—
362C22×C8—31no—
363C22×C8—62no—
364C22×C8—121no—
365C22×C8—121no—
366#126—68no—
367#125—62no—
368#125—62no—
369#123—68no—
370C22⋊Q8—22no—
371C22⋊Q8—41no—
372#121—22no—
373#121—34no—
374#121—41no—
375#121—62no—
376#121—62no—
377#121—68no—
378#121—62no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—62no—
382C4×D4—62no—
383C4×D4—68no—
384#117—34no—
385#117—62no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4#6711yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4#6711yescharacteristic
408C2×C22⋊C4#6711yescharacteristic
409C2×C42—61no—
410C2×C42C22×D311yescharacteristic
411#103—62no—
412#103—62no—
413#103—62no—
414#102—62no—
415#102—62no—
416#102—62no—
417#102—121no—
418#102—121no—
419C22⋊C8—62no—
420C22⋊C8—121no—
421C22⋊C8—121no—
422#95—21no—
423#95—21no—
424#95—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—22no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3#12012yes—
445C23×C3#13512yes—
446C23×C3C22×D411yescharacteristic
447C22×D3—22no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C3×Q8—22no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—41no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—44no—
461C3×D4—48no—
462C3×D4—41no—
463C3×D4—41no—
464C3×D4—84no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—48no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4#12012yes—
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499C2×C3×C4H(5,𝔽2)11yescharacteristic
500C2×C3×C4H(5,𝔽2)11yescharacteristic
501#67—48no—
502#67—84no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—84no—
513D12—22no—
514D12—22no—
515D12—41no—
516D12—41no—
517C4×D3—84no—
518C3⋊C8—41no—
519C3⋊C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—21no—
523C24—61no—
524C24C2×#6711yescharacteristic
525C24C2×#6711yescharacteristic
526#41—28no—
527#41—44no—
528#41—44no—
529#41—44no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8#23712yes—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—32no—
544C2×D4—41no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—64no—
551C2×D4—64no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—81no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—241no—
561C2×D4—241no—
562C2×D4#23712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—64no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—64no—
584C22×C4—241no—
585C22×C4—241no—
586C22×C4—241no—
587C22×C4—241no—
588C22×C4D3×D412yes—
589C22×C4D3×D412yes—
590C22×C4C2×#6711yescharacteristic
591C22×C4C2×#6711yescharacteristic
592C22×C4C2×#6711yescharacteristic
593C22×C4C2×#6711yescharacteristic
594C22×C4C23×D311yescharacteristic
595SD16—124no—
596D8—124no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8—61no—
601C2×C8—61no—
602C2×C8—61no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—124no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—32no—
616C4⋊C4—32no—
617C4⋊C4—32no—
618C4⋊C4—42no—
619C4⋊C4—64no—
620C4⋊C4—64no—
621C4⋊C4—64no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—64no—
631C22⋊C4—64no—
632C22⋊C4—64no—
633C22⋊C4—64no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C42—21no—
637C42—21no—
638C42—64no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3C2×#12011yescharacteristic
661C22×C3#54611yescharacteristic
662C22×C3#54611yescharacteristic
663C22×C3C2×#13511yescharacteristic
664C22×C3#57511yescharacteristic
665C22×C3#57611yescharacteristic
666C22×C3#57711yescharacteristic
667C2×D3—42no—
668C2×D3—42no—
669C2×D3—42no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—22no—
675C3×C4—41no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4#52511yescharacteristic
682C3×C4#53511yescharacteristic
683C3×C4#54611yescharacteristic
684C3×C4#54611yescharacteristic
685Dic3—42no—
686Dic3—42no—
687Dic3—42no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—62no—
708C23—121no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23#93712yes—
715C23#95012yes—
716C23C22×#6711yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721D4—22no—
722D4—22no—
723D4—44no—
724D4—48no—
725D4—41no—
726D4—41no—
727D4—62no—
728D4—62no—
729D4—84no—
730D4—128no—
731D4—121no—
732D4—121no—
733D4—244no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—48no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—244no—
773C2×C4—244no—
774C2×C4#93712yes—
775C2×C4C2×D3×D411yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4C2×#23711yescharacteristic
778C2×C4C2×#23711yescharacteristic
779C2×C4#100411yescharacteristic
780C2×C4#100411yescharacteristic
781C8—121no—
782C8—121no—
783C8—121no—
784C8—121no—
785C2×C3—42no—
786C2×C3—42no—
787C2×C3—82no—
788C2×C3#240411yescharacteristic
789C2×C3#300211yescharacteristic
790C2×C3#301211yescharacteristic
791C2×C3#329711yescharacteristic
792C2×C3#330111yescharacteristic
793C2×C3#330711yescharacteristic
794C2×C3#330911yescharacteristic
795D3—82no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—122no—
818C22—122no—
819C22—122no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22C2×#93711yescharacteristic
825C22#580611yescharacteristic
826C22#580611yescharacteristic
827C22C2×#95011yescharacteristic
828C22#582211yescharacteristic
829C22#583511yescharacteristic
830C22#583711yescharacteristic
831C4—22no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—81no—
837C4—81no—
838C4—122no—
839C4—122no—
840C4—122no—
841C4#558611yescharacteristic
842C4#559111yescharacteristic
843C4#559111yescharacteristic
844C4#559211yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—42no—
848C2—82no—
849C2—242no—
850C2#8258111yescharacteristic
851C2#8292611yescharacteristic
852C2#8342411yescharacteristic
853C2#8349511yescharacteristic
854C2#8351211yescharacteristic
855C2#8353511yescharacteristic
856C2#8357211yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2407C2
socleC23×C3C22×D4
hypercenter#2407D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#5565C2semidirect
2. C3×#2407C2semidirect
3. C2×#5238C2semidirect
4. C2×#5233C2semidirect
5. #71699C2semidirect
6. #71692C2semidirect
7. #71684C2semidirect
8. #71677C2semidirect
9. #71610C2semidirect
10. #69687C2semidirect
11. #69669C2semidirect
12. #69657C2semidirect
13. #69639C2semidirect
14. #69515C2semidirect
15. #69503C2semidirect
67. #2407D3semidirect
127. #930D4semidirect
132. #926D4semidirect
845. C3#23962semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#55652
C3×#24072
C2×#52382
C2×#52332
#716992
#716922
#716842
#716772
#716102
#696872
#696692
#696572
#696392
#695152
#695032
#239623